Windchill doesn't know or care what machine/OS the database is installed on, as long as it can be accessed over the network. So, from that standpoint, there's no problem with what you're suggesting.
The only issue would be with the creation of the Windchill database. Usually, when you install Windchill with a remote database, you install the OCU (Oracle Configuration Utility) on the DB machine first, which creates the Windchill database. But, if you're not able to log into the DB machine directly, then you won't be able to install the OCU.
Are you at least able to SSH into the Oracle machine? If so, you can still create the DB. If you're able to forward an X11 session over SSH, then you can run the PSI and install the OCU on the DB machine through the forwarded X11 session. If you can't forward X11, but have terminal access over SSH, you could manually create the database using the DBCA command line utility. The intructions for using this utility to create the DB can be found in article CS36056.
The only problem is that this command requires a template file. The Windchill DB templates are installed by the OCU. So, if you can't install the OCU, you won't have the templates. However, if you have another machine running Windchill, you can pull the template files out of the OCU directory on that machine. The template files are located in the directory <Base Install Directory>/OCU/db_util/create_db/templates/10g/.